Wood, Ian
(2009)
*
The Ornstein-Uhlenbeck Semigroup in Bounded and Exterior Lipschitz Domains.
*
In: Janas, Jan and Kurasov, Pavel and Naboko, Serguei and Laptev, Ari and Stolz, Gunter, eds.
Methods of Spectral Analysis in Mathematical Physics.
Operator Theory: Advances and Applications, 186
.
Birkhaeuser, Basel, pp. 415-435.
ISBN 9783764387549.
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Official URL http://dx.doi.org/10.1007/978-3-7643-8755-6_21 |

## Abstract

We consider bounded Lipschitz domains Ω in ℝ n . It is shown that the Dirichlet-Laplacian generates an analytic C 0-semigroup on L p (Ω) for p in an interval around 2 and that the corresponding Cauchy problem has the maximal L q -regularity property. We then prove that for bounded or exterior Lipschitz domains Ornstein-Uhlenbeck operators A generate C 0-semigroups in the same p-interval. The method, also allows to determine the domain D(A) of A and, if Ω satisfies an outer ball condition, allows to show L p -L q -smoothing properties of the semigroups.

Item Type: | Book section |
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Subjects: | Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Ian Wood |

Date Deposited: | 09 Apr 2010 10:56 |

Last Modified: | 28 Jul 2014 08:09 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/23941 (The current URI for this page, for reference purposes) |

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